Recent development in Graphics Processing Units (GPUs) has enabled a new possibility for highly efficient parallel computing in science and engineering. Their massively parallel architecture makes GPUs very effective for algorithms where processing of large blocks of data can be executed in parallel. Multidimensional integration has important applications… (More)
We present a memory-efficient algorithm and its implementation for solving multidimensional numerical integration on a cluster of compute nodes with multiple GPU devices per node. The effective use of shared memory is important for improving the performance on GPUs, because of the bandwidth limitation of the global memory. The best known sequential… (More)
Time ordering of interactions in dynamic quantum multi-electron systems provides a constraint that interconnects the time evolution of different electrons. In energy space, time ordering appears as the principal value contribution from the Green function, which corresponds to the asymptotic condition that specifies whether the system has outgoing (or… (More)
We examine how time ordering works in quantum mechanics and in classical mechanics.